Extending WooCommerce cart class is a bit tricky, but possible.
Lets assume you have a plugin and a file class-my-wc-cart.php
with extended cart class inside. Then in the main plugin file you need to do following:
// load your My_WC_Cart class
require_once 'class-my-wc-cart.php';
// setup woocommerce to use your cart class
add_action( 'woocommerce_init', 'wpse8170_woocommerce_init' );
function wpse8170_woocommerce_init() {
global $woocommerce;
if ( !is_admin() || defined( 'DOING_AJAX' ) ) {
$woocommerce->cart = new My_WC_Cart();
}
}
// override empty cart function to use your cart class
if ( !function_exists( 'woocommerce_empty_cart' ) ) {
function woocommerce_empty_cart() {
global $woocommerce;
if ( ! isset( $woocommerce->cart ) || $woocommerce->cart == '' ) {
$woocommerce->cart = new My_WC_Cart();
$woocommerce->cart->empty_cart( false );
}
}
}